A meat cleaver is clasped in his blood-smeared left hand; the other – also stained red with human blood – waves manically as he shouts at the camera, ranting his justification for the atrocity on the streets of south-east London.

At about the same time, in the nearby Musgrave primary school, the headteacher David Dixon ordered a lockdown after seeing the body of a man – believed to be a young soldier – lying on John Wilson street.

If there was any doubt why this young man, who witnesses said was aged in his early 20s and wearing a Help for Heroes T-shirt, had lost his life in such a brutal fashion, that was soon quashed. Shouting the justification of al-Qaida-inspired jihadists across the world, the tall black man, dressed in the dark clothing and beanie hat of urban south London, spat his words to an eyewitness filming on his mobile phone.

"We swear by almighty Allah we will never stop fighting you. The only reasons we have done this is because Muslims are dying every day. This British soldier is an eye for an eye, a tooth for tooth.

'They were crazed, they were animals,' said one eyewitness. Photograph: ITV News

"We must fight them. I apologise that women had to witness this today, but in our land our women have to see the same. You people will never be safe. Remove your government. They don't care about you."

In a few minutes on a cloudy May afternoon, terror had struck again in the UK in a style that counter-terrorist officials have long feared; brutally, out of nowhere and with chilling and horrific effect.

The lives of ordinary members of public going about their daily business were changed for ever as they walked, drove or sat on buses straight into a scene of horror the like of which has never been witnessed on the streets of the capital.

One eyewitness named as James Heneghan saw the whole thing unfold as he drove his girlfriend to work. His voice choking, he had to break off repeatedly as he described on LBC what happened.

"We were coming round the corner into John Wilson Street. Slightly to the left, about 5ft away, there was a Vauxhall, crashed into a sign post. To the left of the car there was two guys with the victim on the floor.

"We thought they were helping him. But next thing, my partner let out an almighty scream. We then saw clearly the two guys with the meat cleaver and knives. They weren't little knives – they were both butcher's-type knives.

"They were hacking this poor guy, literally. We saw it all. They were hacking him – we thought they were trying to remove his organs. They were digging him, cutting him. We jumped out of the car and shouted.

"One of the black guys got in a car, got out a black bag and pulled a handgun out and shouted: 'Get in the car.' He was waving this gun around."

As Heneghan moved his car up the road and called the police, other people gathered on the main street, some shouting for the killers to stop.

Women – a handful of incredibly brave women – were seen standing over the body of the now dead young man, shielding him, covering him, making attempts – sadly far too late – to protect him.

"While I was on the phone to the police they were still hacking away at him," said Heneghan. "They were crazed, they were animals. They dragged the body into the middle of the street and left him there."

For what witnesses said was between 15 and 20 minutes – the timing has not been confirmed by the police – the men waited for the armed response teams they knew were coming. Unarmed officers were behind barriers, waiting too.

Joe Tallant, 20, a local man who said he witnessed the attack, said that a friend's mother comforted the victim, who may have already been dead at that stage. He reported one of the attackers as saying: "No man is coming near this body."

There was little doubt that the attackers wanted witnesses for their macabre act. "They were asking people to take pictures of them. It was like they wanted to be famous or something, but in a stupid way.

"In the time that it took for the police to come, they could have got away, but they just waited. When the cops came, the attackers just walked towards them. They plodded. A lady jumped out and shot them."

Julia Wilders, 51 said that she saw that a car had crashed into a lamppost when she went to investigate.

"My husband said there were two people trying to resuscitate someone. We parked and walked back to have a look and all of a sudden a tall black bloke came up with a gun. My husband said, 'Get back, get back' and we called the police."

She said that one man was dressed all in black with a black cap while the other was dressed in a green jumper. "They looked like they were on drugs," she added.

Her husband, Graham, 50, called the police to alert them to what they believed was an accident.

"After we called the police, I went over to the school to let the school know so the kids wouldn't come out," she said.

As onlookers gathered, one of the men – who were reportedly dancing over the body – rushed up to passengers on a bus.

"He was asking people to take his photograph on the bus," said Heneghan. "He was getting people to take his picture. He was proud of what he had done. Then he was walking up and down with the gun. They were both waiting for something. They were waiting for the armed police to arrive."

As the firearms unit drove in, Heneghan and other eyewitnesses said the men charged them. There were unconfirmed reports that one of the attackers opened fire with his handgun, and then four to six shots rang out from armed police, and the men were felled by a female police marksman.

Graham Wilders said: "All I heard was four shots when the Trojan people turned up. These men actually went for the police with the machetes, knife and handgun.

"I don't think they cared. I don't think they really cared because they went for the police with a handgun."

Dixon, the headteacher at Musgrave, heard the shots ring out as he ran back to his school, and ordered the lockdown. Inside children were playing in the playground. Many had just returned from lunch and were in their last classes before leaving.

"There were lots of police and emergency vehicles and I saw the body lying in the road. We locked the gates, we locked everything down to make sure the children were safe inside. The police helicopter landed in the playground and we helped to direct them where to go.

"The children were asking questions. There was a helicopter flying around – they wanted to know what was going on. But everything was calm. We were able to let the children go home; we kept them safe."

On John Wilson Street, the blood pooled around the body of the victim as paramedics attended him. "I asked the police what they were doing and the police said they had to try, but it was too late," said Heneghan.

Inside the nearby Royal Artillery Barracks, Woolwich officers were checking which personnel were present as reports that the victim of the attack was a soldier spread across social media forums, with videos and photographs of the victim lying prone on the street posted on Twitter and Facebook.

One eyewitness posting on Twitter wrote: "Oh my God!!! The way the Feds took them out!!! It was a female police officer she come out the whip and just started bussin shots … right next to a primary school."

As the government, the security services and the police switched into full counter-terror emergency mode, the people of Woolwich stood around, stunned, some weeping, others shaking their heads. They had witnessed carnage and could not take it in. "My girlfriend is hysterical," said Heneghan, "just hysterical. I'm really worried about her."

Commander Simon Letchford of the Metropolitan police appealed for calm.

"I can understand that this incident will cause community concerns, and I would like to reiterate that we are investigating what has taken place today. There will continue to be an increased police presence in this area, and the surrounding areas this evening. That presence will continue as long as is needed."